# claqsp.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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claqsp.f

## SYNOPSIS

### Functions/Subroutines

subroutine claqsp (UPLO, N, AP, S, SCOND, AMAX, EQUED)
CLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ.

## Function/Subroutine Documentation

### subroutine claqsp (character UPLO, integer N, complex, dimension( * ) AP, real, dimension( * ) S, real SCOND, real AMAX, character EQUED)

CLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ.

Purpose:

``` CLAQSP equilibrates a symmetric matrix A using the scaling factors
in the vector S.
```

Parameters:

UPLO

```          UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored.
= 'U':  Upper triangular
= 'L':  Lower triangular
```

N

```          N is INTEGER
The order of the matrix A.  N >= 0.
```

AP

```          AP is COMPLEX array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the symmetric matrix
A, packed columnwise in a linear array.  The j-th column of A
is stored in the array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.

On exit, the equilibrated matrix:  diag(S) * A * diag(S), in
the same storage format as A.
```

S

```          S is REAL array, dimension (N)
The scale factors for A.
```

SCOND

```          SCOND is REAL
Ratio of the smallest S(i) to the largest S(i).
```

AMAX

```          AMAX is REAL
Absolute value of largest matrix entry.
```

EQUED

```          EQUED is CHARACTER*1
Specifies whether or not equilibration was done.
= 'N':  No equilibration.
= 'Y':  Equilibration was done, i.e., A has been replaced by
diag(S) * A * diag(S).
```

Internal Parameters:

```  THRESH is a threshold value used to decide if scaling should be done
based on the ratio of the scaling factors.  If SCOND < THRESH,
scaling is done.

LARGE and SMALL are threshold values used to decide if scaling should
be done based on the absolute size of the largest matrix element.
If AMAX > LARGE or AMAX < SMALL, scaling is done.
```

Author:

Univ. of Tennessee

Univ. of California Berkeley